3A/3B Mathematics Specialist Class Notes

Curriculum Council curriculum documents: http://www.curriculum.wa.edu.au/internet/Senior_Secondary/Courses/Mathematics_Specialist

Study Topics for MAS 3A

Functions

• The absolute value function
• Function composition
• Domain and range of a function
• Inverse functions
• Domain and range of inverse functions
• Function transformations

Exponentials and Logarithms

• Index laws
• Exponential functions
• Logarithms
• Log functions
• Log laws
• Growth and decay problems

Trigonometry

• Area of a triangle
• Sectors and segments
• Sine and cosine rules
• Triangle inequality
• Radians
• Arc lengths (including latitude and longitude problems)

Polar Coordinates

• Polar coordinates
• Polar and Cartesian conversions

Vectors

• Vectors and scalars
• Vector comparisons: vector equality, opposite vectors, unit vectors and the zero vector.
• Component vectors (including different notations for component vectors)
• Vector magnitude
• Converting vectors between component form and magnitude/angle form
• Adding vectors using the parallelogram law
• Scalar multiplication: multiplying a vector by a scalar
• Relative vectors: relative displacement and relative velocity

Statistics

• The Normal distribution

Study topics for MAS 3B

Functions

• Continuity and Limits
• Derivities
• Differentiability
• Graphs of gradient functions
• Piecewise defined functions
• The chain rule
• Product and quotient rules
• Integrals

Complex numbers

• Imaginary and complex numbers
• Complex roots of quadratics
• The Argand plane
• Complex arithmetic
• Complex conjugates

Exponentials and Logarithms

• Limiting behaviour of exponentials
• Limits and e
• Growth and decay problems
• Derivatives of exponentials and logs

Trigonometry

• Trig functions including concepts of parity, periodicity, complementarity and phase, and the Pythagorean identity.
• Transformations of trig functions
• Trig angle sum and difference identities
• Solving trig functions in a finite domain
• Proving trig identities

Vectors

• Practical vector problems
• Dot product
• Angle between vectors
• Vector equation of a line including point+slope, two point and normal forms
• Vector equation of a circle
• Minimum distance problems